Asked by Michael
Find the Limit of x->1+
x^3 + 1/ x - 1 =?
Please help and explain, I'm really lost.
x^3 + 1/ x - 1 =?
Please help and explain, I'm really lost.
Answers
Answered by
HM
lim (x^3 - 1) / (x - 1)
x -> 1
To evaluate this limit, we must remove the [0/0] form of it. If we were to plug in x = 1 now, we would get [0/0], which alone tells us the limit may exist.
The numerator factors as a difference of cubes.
lim (x - 1)(x^2 + x + 1) / (x - 1)
x -> 1
And look how (x - 1) cancels out.
lim (x^2 + x + 1)
x -> 1
It is now safe to evaluate the limit at x = 1.
1^2 + 1 + 1
1 + 1 + 1
3
x -> 1
To evaluate this limit, we must remove the [0/0] form of it. If we were to plug in x = 1 now, we would get [0/0], which alone tells us the limit may exist.
The numerator factors as a difference of cubes.
lim (x - 1)(x^2 + x + 1) / (x - 1)
x -> 1
And look how (x - 1) cancels out.
lim (x^2 + x + 1)
x -> 1
It is now safe to evaluate the limit at x = 1.
1^2 + 1 + 1
1 + 1 + 1
3
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.